Please help me understand this

The system of equations that is represented by the graph include:

D. y = x - 4

   [tex]y=\frac{x-4}{x+2}[/tex]

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of the red line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 + 5)/(4 + 1)

Slope (m) = 5/5

Slope (m) = 1

At point (4, 0) and a slope of 1, a linear equation for C can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 0 = 1(x - 4)

y = x - 4

Since the rational function has a y-intercept of (0, -2), it would have a vertical asymptote and the denominator would be undefined at x = 2;

[tex]y=\frac{x-4}{x+2}[/tex]

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The arrow is at a height of 48 ft after approx. 3 - √6 s and after 3 + √6 s.

To find the time it takes for the arrow to reach a height of 48 ft, we can use the formula for the height of the arrow:

s = v0t - 16t^2

Here, s represents the height of the arrow, v0 is the initial velocity, and t is the time.

Given that the initial velocity, v0, is 96 ft/s and the height, s, is 48 ft, we can set up the equation:

48 = 96t - 16t^2

Now, let's solve this equation to find the time it takes for the arrow to reach a height of 48 ft.

Rearranging the equation:

16t^2 - 96t + 48 = 0

Dividing the equation by 16 to simplify:

t^2 - 6*t + 3 = 0

We now have a quadratic equation in the form of at^2 + bt + c = 0, where a = 1, b = -6, and c = 3.

Using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values:

t = (6 ± √((-6)^2 - 413)) / (2*1)

t = (6 ± √(36 - 12)) / 2

t = (6 ± √24) / 2

Simplifying the square root:

t = (6 ± 2√6) / 2

t = 3 ± √6

Therefore, the arrow reaches a height of 48 ft after approximately 3 + √6 seconds and 3 - √6 seconds.

In summary, the arrow takes approximately 3 + √6 seconds and 3 - √6 seconds to reach a height of 48 ft, assuming an initial velocity of 96 ft/s.

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Note the complete question is

The height of an arrow shot upward can be given by the formula s = v0*t - 16*t², where v0 is the initial velocity and t is time.How long does it take for the arrow to reach a height of 48 ft if it has an initial velocity of 96 ft/s?  

Solve (t-3)^2=6

The arrow is at a height of 48 ft after approx. ___ s and after ___ s.

The correct equation is sin h° = z ÷ x, which states that the sine of angle A is equal to the ratio of the length of side AB to the length of side AC.

The correct equation relating the angles and segments in triangle ACB depends on the specific trigonometric function and the angle we are considering.

In triangle ACB, angle C is a right angle, which means it measures 90 degrees. The other two angles, angle A and angle B, are complementary angles, meaning their sum is also 90 degrees. Therefore, angle A measures h degrees and angle B measures g degrees, where h + g = 90.

Now let's consider the segments in the triangle. Segment AC measures x, segment CB measures y, and segment AB measures z.

When it comes to trigonometric functions, sine (sin) and cosine (cos) are commonly used. These functions relate the angles and sides of a right triangle.

The correct equation involving the angles and segments can be determined based on the trigonometric function that relates the desired angle to the desired segment.

If we want to relate angle A (measuring h degrees) to the segment AB (measuring z), we can use the sine function. Therefore, the correct equation is:

sin h° = z ÷ x

This equation relates the sine of angle A to the ratio of the lengths of the side opposite angle A (segment AB) and the hypotenuse (segment AC).

In summary, the correct equation is sin h° = z ÷ x, which states that the sine of angle A is equal to the ratio of the length of side AB to the length of side AC.

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Answer:

x = - 1

Step-by-step explanation:

P = [tex]\frac{x-2}{x+1}[/tex]

the denominator of the rational function cannot be zero as this would make it undefined. Equating the denominator to zero and solving gives the value that x cannot be.

x + 1 = 0 ( subtract 1 from both sides )

x = - 1

P is undefined when x = - 1

To determine the minimum sample size required to estimate the proportion of students who bring laptops to campus with a 99% confidence level and a margin of error within five percentage points, we can use the formula:

[tex]n = \frac{(Z^2 \times p \times (1 - p))}{ E^2}[/tex]

Where:

n is the required sample size,

Z is the Z-score corresponding to the desired confidence level,

p is the estimated population proportion (since no prior estimate is available, we use 0.5 as a conservative estimate),

E is the margin of error.

For a 99% confidence level, the Z-score is approximately 2.58 (obtained from the z table).

Plugging in the values:

[tex]n = \frac{(2.58^2 \times 0.5 \times (1 - 0.5))} { (0.05^2)}[/tex]

Simplifying the equation:

n = 663.924

Rounding up to the nearest whole number, the minimum sample size required is approximately 664 students.

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a) The experimental probability of landing on red or yellow is:

P(red or yellow) = 33/40

b) The theoretical probability can be computed as follows:

P(red or yellow)  = 8/10

c) As the number of spins increases: Option A: we expect the experimental and theoretical probabilities to become closer, though they might not be equal.

Theoretical probability represents the likelihood of an event occurring. The theoretical probability of getting heads is 1/2, because we know that the probability of heads and tails on a coin is equal. Experimental probability describes how often an event actually occurred in an experiment.  

a) The experimental probability of landing on red or yellow is:

P(red or yellow) = (20/40) + (13/40) = 33/40

b) The theoretical probability can be computed as follows:

P(red or yellow) = (4/10) + (4/10) = 8/10

c) As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.

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The area of the irregular shape is 34 square feet.

To find the area of the irregular shape, we need to break it down into smaller components and calculate their individual areas.

We will assume the irregular shape is composed of three rectangles.

Rectangle 1: Length = 6 ft, Width = 4 ft.

Area = Length × Width

Area = 6 ft × 4 ft

Area = 24 square feet.

Rectangle 2: Length = 4 ft, Width = 1 ft.

Area = Length × Width

Area = 4 ft × 1 ft

Area = 4 square feet.

Rectangle 3: Length = 1 ft, Width = 6 ft.

Area = Length × Width

Area = 1 ft × 6 ft

Area = 6 square feet.

Total Area = Area of Rectangle 1 + Area of Rectangle 2 + Area of Rectangle 3

Total Area = 24 square feet + 4 square feet + 6 square feet

Total Area = 34 square feet.

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The roster method of the set X ∪ (Y ∩ Z) = {p, q, r, s, 21, 22, 23, 25}

The roster method is defined as a way to show the elements of a set by listing the elements inside of brackets.

A typical example of the roster method is to write the set of numbers from 1 to 5 as {1, 2, 3, 4, 5}.

Therefore,

X = {p, q, r, 21, 22, 23}

Y = {q, s, t, 21, 23, 25}

Z = {q, s, 22, 23, 25}

Therefore, let's find X ∪ (Y ∩ Z) as follows:

(Y ∩ Z) = {q, s, 23, 25}

X = {p, q, r, 21, 22, 23}

Therefore,

X ∪ (Y ∩ Z) = {p, q, r, s, 21, 22, 23, 25}

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